Geometry Worksheet
Name: Ima Key
Sec. 3.2 - Properties of Parallel Lines
Period:
6
Date: 10/28/10
By definition, we know that parallel lines are …
We then discussed one of Euclid’s most important Geometric postulates, the Corresponding < Post:
If two parallel lines are cut by a transversal, then …
Diagram 1: Assume that a || b || c and d || e.
Determine which angles must be
congruent to the identified angle.
Diagram 2: Assume that a || b. What would appear to be true of <1 and <2?
Given: a || b
Prove:
Diagram 3: Assume that a || b. What would appear to be true of <3 and <4?
Given: a || b
Prove:
Diagram 4: Assume that a || b. What would appear to be true of <5 and <6?
Given: a || b
Prove:
Diagram 5: Assume that a || b. What would appear to be true of <7 and <8?
Given: a || b
Prove:
Properties of Parallel Lines:
By definition, we know that …
By postulate, we know that …
Through prove (theorems), we know that …
Diagram 6: Give a term that describes each < pair and determine the relationship between the <s.
Diagram 7: Assume that a || b and b || c.
What would appear to be true of <1 and <2?
What would appear to be true of a and c?
Prove it!!!!!
Given: a || b and b || c
Prove:
Thus, we have proven another property of parallel lines: If two lines are parallel to the same line,
then …
In order to complete the above statement, we needed to assume the converse of the Corr < Post to
be true. Is the converse of a statement ALWAYS true?
Explain?
Therefore, in order for us to guarantee the converse to be true, we either have to prove it or assume it
to be true. Since we assume the Corr < Post to be true(it is a POSTULATE) and then use it to prove
the remaining properties, it only makes sense that we will assume the converse is true and use it too.
Converse of the Corresponding Angle Postulate: If two lines are cut by a transversal such that at
least one pair of corresponding angles are congruent, then …
List 6 ways that you know if two lines are parallel to each other:
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Diagram 8: If <1
Given: <1
<2
<2, what would you assume to be true of lines a and b?